顶点移除后保持总距离的图

Q2 Mathematics

Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI:10.1016/j.endm.2018.06.019

Snježana Majstorović, Martin Knor, Riste Škrekovski

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引用次数: 1

摘要

连通图G的总距离或维纳指数W(G)被定义为G中所有顶点对之间的距离和。1991年，Šoltés提出了一个问题，即找到所有图G，使得等式W(G)=W(G−v)对所有顶点v都成立。到目前为止，唯一已知的具有这个性质的图是循环C11。我们的主要研究对象是这个问题的一个宽松版本:找到当移除一个特定顶点时总距离不改变的图。我们证明有无穷多个图满足这个性质。这给了人们希望，Šoltes的问题可能也有一些不同于C11的解决方案。

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Graphs preserving total distance upon vertex removal

The total distance or Wiener index $W (G)$ of a connected graph G is defined as the sum of distances between all pairs of vertices in G. In 1991, Šoltés posed the problem of finding all graphs G such that the equality $W (G) = W (G - v)$ holds for all their vertices v. Up to now, the only known graph with this property is the cycle C₁₁. Our main object of study is a relaxed version of this problem: Find graphs for which total distance does not change when a particular vertex is removed. We show that there are infinitely many graphs that satisfy this property. This gives hope that Šoltes's problem may have also some solutions distinct from C₁₁.

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来源期刊

Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.